If you have taken a calculus III course at all (looks like you are taking one right now)the questions are reversed and stated as parameterize the following. If you think in a reverse way, you may get some insight.

Look up ellipse in the form of ...oops I'm not supposed to give out the answer!

okay so if you are supposed to square both side of the equation you should get
x^2/9=sin^2(2t)
how did you get y=4sint(2t)?
but if you were to square that you would get y^2/16=sin^2(2t)
then if you add the two equations
x^2/9=y^2/16
x^2/9-y^2/16=0
is that what you mean?